Prof. Dr. Ben Heuer

Institut für Algebra, Zahlentheorie und Diskrete Mathematik
Welfengarten 1
30167 Hannover, Germany

Office: A412
E-Mail: ben.heuer"at"math.uni-hannover.de
Here is a short CV.

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Research

I am a Professor of Algebra at Leibniz Universität Hannover. My research is in arithmetic algebraic geometry. My current projects are related to:

• \(p\)-adic Hodge theory, especially the \(p\)-adic Simpson correspondence
• the \(p\)-adic Local Langlands Program
• the \(p\)-adic geometry of Shimura varieties

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Publications and Preprints

• \(p\)-adic non-abelian Hodge theory for curves via moduli stacks
  with Daxin Xu
  J. Am. Math. Soc., 2025. [ arXiv ]
• The relative Hodge-Tate spectral sequence for rigid analytic spaces
  J. Lond. Math. Soc., 2025. [ arXiv ]
• A \(p\)-adic Simpson correspondence for smooth proper rigid varieties
  Inventiones Math., 2025. [ arXiv ] [expository notes]
• Hodge-Tate stacks and non-abelian \(p\)-adic Hodge theory of v-perfect complexes
  with Johannes Anschütz and Arthur-César Le Bras
  J. Reine Angew. Math. (Crelle), 2025. [ arXiv ]
• \(p\)-adic Simpson correspondences for principal bundles in abelian settings
  with Annette Werner and Mingjia Zhang
  Canad. J. Math., 2025. [ arXiv ]
• The small \(p\)-adic Simpson correspondence in terms of moduli spaces
  with Johannes Anschütz and Arthur-César Le Bras
  Math. Res. Lett. (to appear) [ arXiv ]
• v-vector bundles on \(p\)-adic fields and Sen theory via the Hodge-Tate stack
  with Johannes Anschütz and Arthur-César Le Bras
  Simons Symp. (to appear)[ arXiv ]
• Moduli spaces in \(p\)-adic non-abelian Hodge theory
  J. Algebraic Geom. (to appear) [ arXiv ]
• \(G\)-torsors on perfectoid spaces
  Epijournal Geom. Algebr. (to appear) [ arXiv ]
• The Primitive Comparison Theorem in characteristic \(p\)
  Math. Z., 2024. [ arXiv ]
• Perfectoid spaces. In: Non-Archimedean Geometry and Eigenvarieties
  Editors: Eugen Hellmann, Judith Ludwig, Otmar Venjakob
  Münst. Lect. Math., p159-222, EMS Press 2024. [ preprint ]
• A geometric \(p\)-adic Simpson correspondence in rank one
  Compositio Math., 2024. [ arXiv ]
• Diamantine Picard functors of rigid spaces
  Trans. Amer. Math. Soc. (to appear) [ arXiv ]
• The $p$-adic Corlette-Simpson correspondence for abeloids
  with Lucas Mann, Annette Werner
  Math. Ann., 2022. [ arXiv ]
• Pro-étale uniformisation of abelian varieties
  Preprint 2021 [ arXiv ]
• Line bundles on perfectoid covers: case of good reduction
  Preprint 2021 [ arXiv ]
• Line bundles on rigid spaces in the v-topology
  Forum Math. Sigma, 2022. [ arXiv ]
• Overconvergent Hilbert modular forms via perfectoid modular varieties
  with Christopher Birkbeck, Chris Williams
  Ann. Inst. Fourier, 2022. [ arXiv ]
• Perfectoid covers of abelian varieties
  with Clifford Blakestad, Damián Gvirtz, Daria Shchedrina, Koji Shimizu, Peter Wear, Zijian Yao
  Math. Res. Lett. 29.3: 631-662 (2022). [ arXiv ]
• Cusps and $q$-expansion principles for modular curves at infinite level
  Doc. Math. 27, 2385-2439 (2022) [ arXiv ]
• Perfectoid geometry of $p$-adic modular forms
  PhD thesis 2019, London School of Geometry and Number Theory
• Rigid $\tau$-crystals
  J. Théor. Nombres Bordeaux 29(3):1059-1082, 2017.
  
• All solutions to the immobilizer problem
  with John Conway
  Math. Intelligencer 36(4):78-86, 2014.
  
• Proof-reading guidance in cell tracking by sampling tracking-by-assignment models
  with Martin Schiegg, Carsten Haubold, Steffen Wolf, Ulrich Koethe, Fred A Hamprecht
  In Biomedical Imaging (ISBI), 2015 IEEE 12th International Symposium
  

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Talks and Lecture Notes

• Here are the notes for a minicourse on the \(p\)-adic Simpson correspondence for projective varieties that I gave at the workshop Complex and p-Adic Simpson Correspondence at the Brin Mathematics Research Center in Nov 2025.
• For a broader explanation of what \(p\)-adic non-abelian Hodge theory is about, here is a recording of an introductory talk that I recently gave for a number-theoretic audience (from Journées Arithmétiques 2025).
• Here are the notes for a course on perfectoid spaces that I gave at the Spring School on non-archimedean geometry and eigenvarieties in Heidelberg in 2023.
• Here are the lecture notes for a course on rigid analytic geometry that I gave at the University of Bonn in 2022. Thanks very much to Matthew Stevens for TeXing and for letting me share them here!

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Teaching and Seminars

• Im Sommersemester 26 halte ich die Vorlesung Lineare Algebra II,
  sowie ein Proseminar Darstellungstheorie endlicher Gruppen
  (Hinweise zu Programm und Anmeldung des Proseminars finden Sie hier),
  sowie ein Seminar homologische Algebra
  (Hinweise zu Programm und Anmeldung des Seminars finden Sie hier) .
• Im Wintersemester 25/26 halte ich die Vorlesung Lineare Algebra I, sowie die Vorlesung Zahlentheorie und Kryptographie.
• Im Sommersemester 2025 halte ich die Vorlesung perfektoide Räume, Do 14-16 Uhr, in Raum 310. Die Vorlesung orientiert sich an meinem Skript.
• Im Sommersemester 2025 bin ich Assistent für die Lineare Algebra 2 bei Prof. Werner. Die Website der Vorlesung ist hier.
• Im Wintersemester 24/25 organisiere ich mit Prof. Werner ein Seminar Zahlentheorie und kommutative Algebra. Das Programm finden Sie hier.
• Im Wintersemester 23/24 habe ich mit Prof. Werner ein L3-/Proseminar Quadratische Formen organisiert. Das Programm finden Sie hier hier. Außerdem haben wir ein L3-/Proseminar Geschichte der Mathematik veranstaltet.
• In the summer term 2023, with Annette Werner and Katharina Hübner, we organised a research seminar (GAUS seminar) on Non-archimedean Geometry. The seminar page can be found here.
• Im Sommersemester 2023 war ich Assistent für die Lineare Algebra 2 bei Prof. Werner. Die Website der Vorlesung ist hier.
• Im Wintersemester 22/23 habe ich ein L3-Seminar an der Goethe Universität Frankfurt zum Thema Geschichte der Mathematik veranstaltet. Die Liste der Vorträge finden Sie hier.
• Im Wintersemester 22/23 habe ich mit Prof. Annette Werner ein Proseminar/L3-Seminar an der Goethe Universität Frankfurt zum Thema Beweismethoden veranstaltet.
• In the summer term 22, I taught a lecture course on Rigid Analytic Geometry at the University of Bonn. The course gave an introduction to non-archimedean geometry by discussing in detail Tate's rigid analytic spaces. Thanks very much to Matthew Stevens for TeXing lecture notes and for letting me share them with you here!

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Events

• I co-organised the student conference GROW@Frankfurt 2025 for all students of underrepresented genders who are interested in doing a PhD in mathematics.
• With Johannes Anschütz and Arthur-César Le Bras, we organised a workshop on the recent work of Lue Pan, from 20-25th November 2022 at Maison Du Kleebach. Here is the program.
• In 2022 and 2023, I co-organised the conference "Graduate Opportunities for Women (GROW)" in Bonn. Details can be found here.
• With Mingjia Zhang I organised a Kleine AG on 12 March 2022. Details and notes can be found here.

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Last update: November 2025, Ben Heuer